Uniqueness and continuous dependence on the initial temperature are proved for a onedimensional, quasistatic and frictionless contact problem in linear thermoelasticity. First the problem is reformulated in such a way that it decouples. The resulting problem for the temperature is a nonlinear integro-differential equation. Once the temperature is known the displacement is recovered from an appropriate variational inequality. Uniqueness is proved by considering an integral transform of the temperature. The steady solution is obtained and the asymptotic stability is shown. It turns out that the asymptotic behaviour and the steady state are determined by a relation between the coupling constant a and the initial gap.
Email your librarian or administrator to recommend adding this journal to your organisation's collection.
* Views captured on Cambridge Core between September 2016 - 24th May 2017. This data will be updated every 24 hours.